Everton had to come from behind twice but earned an opening-day point thanks to a Ross Barkley rocket and Arouna Kone's first Goodison Park goal.
Having dominated the game for large periods, a draw was the least the Blues deserved - but Roberto Martinez's men will feel it could so easily have been more.
Mexican Miguel Layun fired the newly-promoted visitors ahead on 14 minutes but Everton eventually hit back when substitute Kone teed up Barkley to thump an unstoppable first-time effort past Hornets stopper Heurelho Gomes with 14 minutes to play.
But the day one drama was far from over. Odion Ighalo's composed 83rd-minute strike left Tim Howard helpless and Goodison stunned.
Yet, Kone - boldly thrown on by Martinez for left-back Brendan Galloway - nipped down the inside right channel with four minutes remaining and calmly slotted the ball across goal and into the bottom corner.
The pre-match news was mixed for Martinez. On the plus side, last season's top scorer Romelu Lukaku shook off a tight hamstring in time to start, however the Toffees boss lost left-back Leighton Baines to a training ground ankle injury suffered on the eve of the campaign.
Winger Gerard Deulofeu was also absent having failed to overcome his own hamstring injury in time, though Kevin Mirallas and John Stones, as expected, took their places despite limping off against Villarreal six days earlier. There was also a first-team debut handed to summer arrival Tom Cleverley.
Predictably, Watford - starting only their third ever Premier League campaign - looked lively from the off.
Everton had the baulk of the possession but the Hornets weren't shy in swarming forward when they had the chance - and it led to Layun connecting with a cross from the left and rifling his side in front from 12 yards.
An immediate reply almost came through Gareth Barry but the veteran midfielder saw his header from Barkley's corner acrobatically tipped over by Gomes.
The Brazilian stopper later denied Barkley, again calling on his agility to palm away a long-range effort from underneath his crossbar.
After the break, Mirallas almost caught out Gomes with a cross that swirled goalwards, before Lukaku failed to find the target after getting his head to a dangerous ball in from the impressive Barkley.
But Martinez felt his side needed more. On came Kone for Galloway, with Barry switching to left-back and the Ivorian going forward to support Lukaku in attack.
The striker's first involvement was to head Cleverley's cross high and wide into the Gwladys Street - but his next contribution was key.
Trapping a cross from Seamus Coleman, Kone stopped the ball dead and laid it on perfectly for the loitering Barkley. Twenty-five yards out, the England man's shot was simply unstoppable.
Ighalo then danced through and lashed home to spread despair across Goodison. But Kone had the last word, his cool finish salvaging a point that was no less than he - and Everton - deserved.